For the latter of course you have to enter the class center in your CSS stylesheet. Since Sigil changes a lot between version, I wouldn't be surprised that the sgc-1 doesn't work anymore. But Valloric could confirm if this is the case.

You're second point can be a problem of a too large image or hard-defined page-breaks. I do not know how stanza works, but you could try to fiddle with CSS elements like 'page-break-before: never' or alike.